 # ODBAC is a fixed rectangular conductor of negligible resistance (CO is not connected) `
Question:

ODBAC is a fixed rectangular conductor of negligible resistance (CO is not connected) and OP is a conductor which rotates clockwise with an angular velocity ω.

The entire system is in a uniform magnetic field B whose direction is along the normal to the surface of the rectangular conductor ABDC. The conductor OP is in

electric contact with ABDC. The rotating conductor has a resistance of λ per unit length. Find the current in the rotating conductor, as it rotates by 180°.

Solution:

(i) When the position of the rotating conductor is assumed to be at the time interval t = 0 to t = π/4ꞷ

We get current I = 1/2 Bl2ꞷ/λl sec2 ꞷt cos ꞷt = Blꞷ/2λ cos ꞷt

(ii) When the position of the rotating conductor is at time interval π/4ꞷ < t < 3π/4ꞷ

We get current I = 1/2 Blꞷ/λ sin ꞷt

(iii) When the position of the rotating conductor is at time interval 3π/4ꞷ < t < π/ꞷ

We get current I = 1/2 Blꞷ/ λ sin ꞷt